# Trying to solve a second order differential equation. Your advices

**URL:** <https://discourse.julialang.org/t/trying-to-solve-a-second-order-differential-equation-your-advices/41162>\
**Category:** Optimization (Mathematical)\
**Created:** [June 10, 2020, 9:04pm UTC](https://discourse.julialang.org/t/trying-to-solve-a-second-order-differential-equation-your-advices/41162 "2020-06-10T21:04:51Z")\
**Posts on this page:** 1\
**Showing post:** 4

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**Author:** ![aquarelle332](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/aquarelle332/32/20816_2.png) [@aquarelle332](https://discourse.julialang.org/u/aquarelle332)\
**Post date:** [June 21, 2020, 11:16am UTC](https://discourse.julialang.org/t/trying-to-solve-a-second-order-differential-equation-your-advices/41162/4 "2020-06-21T11:16:20Z")

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Hello dear all,

Continuing my work on the Rayleigh-Plesset equation, I wrote this code:

```julia
using OrdinaryDiffEq, Plots

#SI units
#external parameters
Pₕ = 1.01325e5 #hydrostatic pressure (Pa)

#Parameters (liquid = water)
Pᵥ = 2.5e3 #vapour pressure (Pa)
σ = 73.0e-3 #surface tension (N/m)
ρ = 1000.0 #volumic mass (Kg.m-3)
η = 1.0e-3 #dynamic viscosity (Pa.s)

#Parameter (gas = Ar)
γ = 1.666 #polytropic ratio (-)

#Acoustic Parameters
Pₐ = 1.3e5 #acoustic pressure (Pa)
fₐ = 2.0e4 #acoustic frequency (s-1)

#Initial conditions
R₀ = [4.0e-6] #initial radius (m)
dR₀ = [1.0e-2] #initial radial velocity (ms-1)
tspan = (0.0,150.0e-6) #(s) -- 1 acoustic cycle = 50 μs

#Num
function rpnnp(ddR, dR, R, p, t)
    @. ddR = (1/ρ*R)*((Pₕ-Pᵥ-(2*σ/R₀))*(R₀/R)^(3*γ)-(4*η*dR/R)-(2*σ/R)-Pₕ+Pᵥ-p(t)) - (1.5*dR*dR)/R
end

P = t->Pₐ*sin(2*pi*fₐ*t + pi/2) #external acoustic wave

probleme = SecondOrderODEProblem(rpnnp, dR₀, R₀, tspan, P)
solution = solve(probleme, DPRKN6())

@show solution.t
@show solution.u

#graph
plot(solution, vars=(2), linewidth=2,
        xaxis = "t ", yaxis = "R",
        framestyle = :box)

```

I am expecting a result like in the 4th graph concerning the “radius versus the time” curve:

![Rayleigh-Plesset_R-t](https://global.discourse-cdn.com/julialang/original/3X/2/7/271ac8fecbe43e84e0c789c16f24a10c86b1b4f6.png)

However with the code as above the bubble radius evolves hardly.  
Do you have a suggestion since I do not see where my error is.  
Thank you in advance,  
Thierry

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